Question

giving a test to a group of students, the table below summarizes the grade earned by gender.

	a	b	c	total
female	13	19	3	35
total	27	37	23	87

if one student is chosen at random, find the probability that the student earned grade b given the student is male. round your answer to four decimal places.

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(B|A)=\frac{P(A\cap B)}{P(A)}$. In the context of the table, if $A$ is the event that the student is male and $B$ is the event that the student earned grade B, then $P(B|A)=\frac{\text{Number of male students with grade B}}{\text{Total number of male students}}$.

Step2: Identify relevant values from the table

The number of male students with grade B is 18, and the total number of male students is 52.

Step3: Calculate the probability

$P=\frac{18}{52}\approx0.3462$

Answer:

$0.3462$